For #"barium carbonate"#, #"barium oxide"#, #"magnesium oxide"#, and #"magnesium chloride"#, which salt is likely to exhibit the greatest lattice enthalpy?
We assess the lattice enthalpy of each species by (i) the size of the ions involved, and (ii) the charges on the ions involved.
For (i), the smaller the ions, the greater should be the resultant lattice enthalpy; for (ii), the more highly charged the individual ions, the greater should be the resultant lattice enthalpy.
Size is minimized, and charge is maximized in the case of magnesium oxide.
Note that as a chemist, as a physical scientist, you should look for the data that informs this argument. In other words, you have to interpret the experimental result.